The numerical solutions of some linear and nonlinear fractional differential equations

This study consist of the five chapters. In the first chapter, it has been given informations on the solution techniques and one the historical structures of differential equations with fractional order was given and some information on the solution techniques were alsopresented. In chapter two, some fundamental definitions and theorems which are necessary in this study was introduced. In chapter three, the general structures of fractional Adams–Bashforth–Moulton Method, Extended Trial Equation Method, Homotopy Analysis Method, Modified Kudryashov Method and Modified Trial Equation Method were. In chapter four, the analytical and numerical solutions of fractional differential equations, Rosenau–Hyman equation with fractional order, Generalized Fisher equation with fractional order and Time-fractional Generalized Burgers equation with fractional order were obtained. Additionally, the numerical data tables concerning with the numerical results for every differential equations were constructed and the absolute errors related with this equation were calculated and the graphics were scathed in 2D and 3D spaces. In chapter five, it has been given a conclusion about techniques used by taking into account analytical, numerical and approximate solutions obtained in this study.